2024/12/17 by M. Chellali, J.C. Valenzuela, Chellali, M. +7 · 2 citations
Economics, Econometrics and Finance · #Game Theory and Voting Systems
paper · pdf · doi:10.48550/arxiv.2412.18623
A set S⊆ V in an isolate-free graph G is a total restrained dominating set, abbreviated TRD-set, if every vertex in V is adjacent to a vertex in S, and every vertex in V∖ S is adjacent to a vertex in V∖ S. A total restrained coalition is made up of two disjoint sets of vertices X and Y of G, neither of which is a TRD-set but their union X∪ Y is a TRD-set. A total restrained coalition partition of a graph G is a partition Φ=\V1, V2,…,Vk\ such that for all i ∈ [k], the set Vi forms a total restrained coalition with another set Vj for some j, where j∈ [k]∖i. The total restrained coalition number Ctr(G) in G equals the maximum order of a total restrained coalition partition in G. In this work, we initiate the study of total restrained coalition in graphs and its properties.